One honest race result contains, in embryo, your times at every other distance — if the scaling law between them is respected. This Training Pace Calculator applies the Riegel formula to a recent performance and predicts equivalent times and paces for the 5K, 10K, half marathon and marathon.
The Riegel Formula and the Worked Example
Peter Riegel’s 1977 relation — fitted from world-record progressions and validated on mortal runners ever since — says equivalent performances scale as T₂ = T₁ × (D₂/D₁)^1.06: double the distance and the time more than doubles, because fatigue’s tax compounds. Feed it a 25:00 5K (1,500 seconds): the 10K prediction is 1500 × 2^1.06 = 1500 × 2.085 = 52:07 (a 5:13/km pace); the half marathon, 1500 × (21.0975/5)^1.06 = 1:55:00 (5:27/km); the marathon, 1500 × (42.195/5)^1.06 = 3:59:47 (5:41/km). Read the paces in the answers and the law becomes visible: each step up in distance surrenders a few seconds per kilometre, and the size of the surrender is the exponent talking. A runner whose real results beat the Riegel spread is endurance-leaning (or undertrained for speed); one whose long results sag behind it is speed-leaning or undertrained for the long work — the formula doubles as a diagnostic, and coaches have used the gap between predicted and actual marathon times to detect insufficient long-run volume for decades. The predictions assume equivalent preparation and conditions across distances: they answer “what is this performance worth elsewhere,” not “what will you run in July on a hilly course after a poor winter,” and the note under the calculator repeats the point because it is the difference between a benchmark and a promise.
From Predictions to Training Paces
The predicted times are the raw material; training paces are what they are cooked into. The standard translations, stated as offsets from the predicted race paces: easy and long-run pace sits about 60–90 seconds per kilometre slower than marathon pace for most club runners (conversation pace — the calculator’s marathon line minus nothing but your restraint); threshold (tempo) pace is approximately your predicted 10K-to-half-marathon pace region, often taken as the pace you could race for about one hour — for the example runner, between 5:13 and 5:27/km; interval pace for VO₂ work tracks the 5K prediction (5:00/km in the example); repetition pace for economy work runs a few seconds per 400 faster still. Different schools (Daniels’ VDOT tables most famously) formalize the same offsets into printed pace bands per performance level — Daniels’ system is, at its core, this same equivalence fitted slightly differently and tabulated beautifully — and the working runner can live on the calculator’s four lines plus the offsets above without apology. Two disciplines protect the translation: train the current fitness the calculator describes (recompute after each benchmark race; paces from last season’s shape are a costume, not a plan), and let the easy days obey the easy offset even when the legs feel heroic — the entire architecture of modern endurance training is hard days hard enough and easy days easy enough, with arithmetic, this arithmetic, drawing the border.
The Formula’s Limits, Stated Plainly
Riegel’s exponent is a population average wearing a crown, and its boundaries are worth knowing. Individual exponents vary: elite endurance athletes sit nearer 1.05, recreational runners often nearer 1.08–1.10 across the 5K-to-marathon span — refit yours from two real results (exponent = ln(T₂/T₁) / ln(D₂/D₁)) and the calculator’s predictions tighten to you personally; two data points is all the personalization costs. Distance range: the law was fitted on roughly 1,500 m to marathon performances — push it to 800 m or to 100-mile ultras and other physics (anaerobic capacity at one end, fueling and terrain at the other) takes the pen. Course and conditions are invisible to it: a windy point-to-point, a hilly profile, altitude and heat each tax the longer distances disproportionately, which is why predictions made from a flat, cool benchmark should be carried into a hard course with a percentage of humility. Preparation specificity is the deepest limit: the formula predicts the equivalent of your demonstrated fitness, and a 5K runner who has never run past 15 km does not own the marathon prediction until the long runs are banked — the number is the ceiling the training must reach for, and the long run, the tempo and the weeks are how ceilings become floors.
A Second Benchmark: The 45-Minute 10K Runner
Run the same law from a different start line to see its personality. A 45:00 10K predicts: 5K 21:35 (4:19/km), half marathon 1:39:17 (4:42/km), marathon 3:27:01 (4:54/km). Notice two things. First, the marathon figure’s neighbourhood: 3:27 from a 45-minute 10K is the exchange rate every experienced runner carries intuitively — the formula’s authority comes from how boringly it agrees with the sport’s folklore once both are made precise. Second, the pace decay pattern compresses as fitness rises: this runner surrenders 23 seconds per kilometre from 5K to 10K pace and only 12 more from half to marathon, while the 25:00 5K example surrendered 13 and then 14–18 — the exponent is one law, but its visible bite depends on where on the curve it catches you, which is why comparing raw pace drops across runners of different levels misleads. If you own two of these four results in reality, fit your personal exponent (the Limits section shows the one-line calculation) and the whole table becomes a portrait instead of a population average — the single most valuable upgrade a season of racing data can buy this page.
Race-Day Arithmetic: Splits and Miles
Two conversions turn the predictions into a race plan. Splits: an even-paced marathon at the prediction is the simplest plan that respects physiology — our 25:00 5K runner’s 3:59:47 divides into halves of about 1:59:53, 10K segments of about 56:47, and kilometres ticking at 5:41 like a metronome; a slight negative split (first half 30–60 seconds slower) is the standard refinement, buying glycogen insurance at the cost of a marginally faster second half the fitness already priced. Write the per-5K splits on the arm or the pacer band from this page’s numbers, not from the goal time’s — the difference between a plan and a wish is which column you copied. Miles: for runners whose watches and road markers speak miles, multiply the per-kilometre pace by 1.609: the example’s marathon pace 5:41/km is 9:09 per mile, the 5K pace 5:00/km is 8:03 per mile, and threshold’s 5:13–5:27 band is 8:24–8:46 per mile. Race predictors feel abstract in kilometres and personal in miles for a large share of the sport’s population — the formula does not care which unit carries it, and neither should the training log, as long as one log picks one unit and keeps it.
Heat: The Adjustment Every Summer Demands
One environmental tax deserves its own line because it arrives every year on schedule: heat. The predictions assume the cool, still conditions of a good benchmark day, and the widely used Galloway adjustment schedule prices a hot race day against them for marathon-pace running: no penalty up to about 60°F, then roughly 30 seconds per mile slower for each 5°F band above it — about a minute a mile at 70°F, two at 80°F, and run-walk territory beyond. Apply it to the plan, not the ego: a 3:59:47 prediction meeting a 75°F start line is honestly a 4:10–4:15 race, and the runner who re-prices at the expo finishes strong while the runner who defends the cool-weather number meets the last 10K in a state the formula never endorsed. The calculator’s outputs are the fitness; the weather is a multiplier the day supplies.
Common Mistakes
Entering a goal time and calling the outputs predictions (the formula translates performances, it does not grant wishes). Running training paces from an old or downhill-aided benchmark. Treating the marathon prediction as guaranteed from a single 5K without the long-run base — the formula assumes equivalent preparation. Setting interval pace equal to 5K goal pace rather than current 5K pace. And ignoring the diagnostic: if your marathon misses the prediction by 20 minutes while your 10K matches it, the gap is the training review — it is almost never the formula.
Related Tools
Continue with the Running Calorie Calculator, the VO2 Max Calculator, the Swim Time Converter, or browse the full Sports Calculators hub.
Frequently Asked Questions
How does the Riegel formula predict race times?
T₂ = T₁ × (D₂/D₁)^1.06. The exponent above 1 encodes fatigue: longer races are run at slower paces. A 25:00 5K predicts 52:07 for 10K, 1:55:00 for the half marathon and 3:59:47 for the marathon — assuming equal preparation and conditions.
What pace should my easy runs be?
Roughly 60–90 seconds per kilometre slower than your predicted marathon pace — genuinely conversational. For the example runner (marathon pace 5:41/km), that is about 6:40–7:10/km, which feels too slow to most new runners and is exactly right.
What is threshold pace?
About the fastest pace you could race for an hour — between your predicted 10K and half-marathon paces. It is the “comfortably hard” of tempo runs, and the most valuable pace in the endurance toolbox.
How accurate is Riegel for the marathon?
For runners trained for the distance, typically within a few percent. It overpromises for runners whose long-run base is missing — the prediction reflects the fitness shown, and marathon fitness specifically includes durability the 5K cannot demonstrate. Use it as the target the training must earn.
Can I personalize the exponent?
Yes, from two real results: exponent = ln(T₂/T₁) ÷ ln(D₂/D₁). Recreational runners often land near 1.08–1.10, elites nearer 1.05. Your own exponent makes cross-distance predictions noticeably tighter than the universal 1.06.
My marathon is much slower than predicted. Why?
Almost always preparation, not arithmetic: insufficient long-run volume, fueling, or a harder course/day. The mismatch is the classic diagnostic — build the long run and the prediction becomes reachable; the formula has been validated on prepared runners for nearly fifty years.